Define average (mean) life of a radioactive substance. How are half-life and average life-related?

Define two units of radioactivity. How are they related?

The ionising power of $\beta$-particles is less compared to $\alpha$-particles but their penetrating power is more, why?

The mass of $\beta$-particles is higher than the mass of electrons obtained by other sources, whereas $\beta$-particles are also electrons. Why?

Copy and complete the following table for a radioactive element whose half-life is $10$ minutes. Assume that you have $30 \mathrm{g}$ of this element at $t=0$.

Complete the following table for a radioactive element whose half-life is $5$ minutes. Assume that you have $32 \mathrm{g}$ of this element at start, i.e., at $t=0$.

Now, using this data, plot the "decay curve".

Starting with the law of radioactive disintegration, show that: $N=N_0 e^{-\lambda t}$, where the terms have their usual meaning.

Define half-life of a radioactive substance. Establish a relation between half-life $t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ and decay constant $\lambda$.